Let (x,y,z)xyz(x,\,y,\,z) be any point of the ellipsoid. The squarex2+y2+z2superscriptx2superscripty2superscriptz2x^{2}\!+\!y^{2}\!+\!z^{2} of the distance of this point from the midpoint(0, 0, 0)0 0 0(0,\,0,\,0) has under the constraints

with which the extremum points (x,y,z)xyz(x,\,y,\,z) can be evaluated. The corresponding values of fffare 10 and 75177517\frac{75}{17}, whence the major semi-axis is 1010\sqrt{10} and the minor semi-axis 5⁢25517525517\frac{5\sqrt{255}}{17}.